Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations

We determine the electronic structure of a graphene sheet on top of a lattice-matched hexagonal boron nitride $\left(h\text{−}\mathrm{B}\mathrm{N}\right)$ substrate using ab initio density functional calculations. The most stable configuration has one carbon atom on top of a boron atom, and the other centered above a BN ring. The resulting inequivalence of the two carbon sites leads to the opening of a gap of $53\mathrm{meV}$ at the Dirac points of graphene and to finite masses for the Dirac fermions. Alternative orientations of the graphene sheet on the BN substrate generate similar band gaps and masses. The band gap induced by the BN surface can greatly improve room temperature pinch-off characteristics of graphene-based field effect transistors.

Figure 1

(Color online) The three inequivalent orientations of single-layer graphene on a $h\text{−}\mathrm{B}\mathrm{N}$ surface. Left, side view; right, top view.

Figure 2

(Color online) Total energy $E$ of graphene on $h\text{−}\mathrm{B}\mathrm{N}$ surface for the three configurations (a), (b), and (c) as a function of the distance between the graphene sheet and the top $h\text{−}\mathrm{B}\mathrm{N}$ layer.

Figure 3

(Color online) Band structure along the $\Gamma K$ and $KM$ directions in reciprocal space, and total and projected densities of states (DOSs) for the relaxed structure (c) of graphene on $h\text{−}\mathrm{B}\mathrm{N}$. Carbon, boron, and nitrogen projected DOSs are shown, with a projection on the $p$ states in plane (red and/or thick gray lines) and out of plane (blue and/or thin gray lines). The inset is a magnification of the bands around the $K$ point, where the gap opens.

Figure 4

(Color online) The values of the gaps for the three configurations (a), (b), and (c) as a function of the distance between the graphene sheet and the top $h\text{−}\mathrm{B}\mathrm{N}$ layer. The calculated equilibrium separations are indicated by vertical arrows.